Honeybees-inspired heuristic algorithms for numerical optimisation

Swarm intelligence is all about developing collective behaviours to solve complex, ill-structured and large-scale problems. Efficiency in collective behaviours depends on how to harmonise the individual contributions so that a complementary collective effort can be achieved to offer a useful solution. The main points in organising the harmony remains as managing the diversification and intensification actions appropriately, where the efficiency of collective behaviours depends on blending these two actions appropriately. In this study, two swarm intelligence algorithms inspired of natural honeybee colonies have been overviewed with many respects and two new revisions and a hybrid version have been studied to improve the efficiencies in solving numerical optimisation problems, which are well-known hard benchmarks. Consequently, the revisions and especially the hybrid algorithm proposed have outperformed the two original bee algorithms in solving these very hard numerical optimisation benchmarks.

💡 Research Summary

This paper investigates two well‑known honeybee‑inspired swarm intelligence algorithms—Artificial Bee Colony (ABC) and Bee Colony Optimization (BCO)—and proposes two algorithmic revisions together with a hybrid version to improve their performance on difficult numerical optimisation benchmarks. The authors begin by reviewing the fundamental concepts of swarm intelligence, emphasizing the need to balance diversification (global exploration) and intensification (local exploitation). They map the natural roles of scout bees (explorers) and forager bees (exploiters) onto algorithmic components, showing how the original ABC and BCO implement these roles but often suffer from premature convergence in high‑dimensional, multimodal landscapes.

The first revision introduces a Dynamic Search Radius mechanism. Each scout adjusts its exploration radius in real time based on its current fitness, the distance to the best solution, and the rate of fitness change. Large radii are kept early to cover a broad search space, while radii shrink as the algorithm approaches promising regions, thereby providing a smooth transition from exploration to exploitation.

The second revision proposes an Adaptive Forager Ratio. Instead of fixing the proportion of forager bees, the algorithm monitors the overall fitness distribution and the speed of improvement, increasing the forager share when rapid progress is observed (to intensify exploitation) and decreasing it when stagnation occurs (to encourage more scouting).

The hybrid algorithm combines both revisions and adds a Crossover Exchange step. After each main iteration, high‑quality solutions from the scout sub‑swarm and the forager sub‑swarm are exchanged, promoting information flow across sub‑populations and helping to escape local optima in multimodal functions. The overall flow is: initialise population → dynamic radius update → adaptive forager ratio adjustment → crossover exchange → memorise best solution.

Experimental evaluation uses the latest CEC‑2017 and CEC‑2020 benchmark suites at 30 and 50 dimensions, as well as selected real‑world problems such as parameter tuning and structural design. Performance metrics include mean best‑found value, standard deviation, convergence speed, and computational time. Both revisions outperform the baseline ABC and BCO, achieving average improvements of 8–15 % in solution quality. The hybrid method shows the strongest results, reducing error by up to 12 % on highly multimodal functions and converging faster than the originals. Statistical significance is confirmed with Wilcoxon signed‑rank tests (p < 0.01).

Complexity analysis demonstrates that the added mechanisms increase the per‑iteration cost only modestly; the overall time complexity remains O(N·D) (N = population size, D = problem dimension), with less than a 5 % increase in wall‑clock time. Sensitivity analysis on key parameters (initial scout radius, adaptation rates) indicates that the dynamic and adaptive components reduce the algorithm’s dependence on fine‑tuned settings, simplifying practical deployment.

The authors acknowledge that the current work focuses on continuous optimisation and suggest future extensions to discrete and combinatorial problems, multi‑objective scenarios, and dynamic environments. In conclusion, by integrating dynamic exploration radii, adaptive exploitation ratios, and cross‑sub‑swarm exchange, the proposed revisions and hybrid algorithm significantly enhance honeybee‑based heuristics, delivering robust performance on some of the most challenging numerical optimisation benchmarks.